GATE 2023 EE – Question 39
A 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is −400 W and the line current is $I_R=2$ A (rms), then the power factor of the load per phase is
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Correct answer: (C) 0.866 leading
Explanation
The wattmeter has its current coil in line R and its potential coil across Y–B. With $V_{RN}$ as reference, $V_{YB}=400\angle-90^\circ$ and $I_R=2\angle-\varphi$. The reading is $W=400\times2\cos(-90^\circ+\varphi)=800\sin\varphi$. Setting $800\sin\varphi=-400$ gives $\sin\varphi=-0.5$, so $\varphi=-30^\circ$: the current leads, and the power factor is $\cos30^\circ=0.866$ leading.